Mobile ferroelectric single domain wall implementation of a symmetric resistive processing unit

ABSTRACT

A method of fabricating a symmetric element of a resistive processing unit (RPU) includes forming a substrate with a channel region connecting two doped regions, and forming a source above one of the two doped regions and a drain above the other of the two doped regions. A gate is formed above the channel region, and a bar ferroelectric is disposed above the channel region and below the gate.

BACKGROUND

The present invention relates to analog memory elements, and morespecifically, to a mobile ferroelectric single domain wallimplementation of a symmetric resistive processing unit (RPU).

Many computer-implemented applications are computationally intensive andrequire parallel processing. For example, in machine learning orsupervised learning, deep neural network (DNN) training techniquesrequire memory calls that can add up over billions of cycles and, thus,benefit from fast memory access. RPUs are arrays of memory elements thatcombine processing and non-volatile memory and can fetch data as fast asit is processed at lower voltages compared to more traditionalnon-volatile memory (NVM) devices.

SUMMARY

According to embodiments of the present invention, a method offabricating a symmetric element of a resistive processing unit (RPU)includes forming a substrate with a channel region connecting two dopedregions, and forming a source above one of the two doped regions and adrain above the other of the two doped regions. A gate is formed abovethe channel region, and a bar ferroelectric is disposed above thechannel region and below the gate.

According to other embodiments of the invention, a method of obtaining amobile ferroelectric single domain wall implementation of a symmetricresistive processing unit (RPU) includes applying a positive pinningvoltage to a first end of a bar ferroelectric, and applying a negativepinning voltage to a second end of the bar ferroelectric. The second endis opposite the first end. The method also includes applying positivepulses across the bar ferroelectric to achieve the single domain wall,and applying additional positive pulses across the bar ferroelectric tomove the single domain wall in a first direction.

According to yet other embodiments of the invention, a symmetric elementof a resistive processing unit (RPU) includes a substrate with a channelregion connecting two doped regions, a source above one of the two dopedregions, and a drain above the other of the two doped regions. A gate isabove the channel region, and a bar ferroelectric is above the channelregion and below the gate.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter which is regarded as the invention is particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The forgoing and other features, and advantages ofthe invention are apparent from the following detailed description takenin conjunction with the accompanying drawings in which:

FIG. 1 is a bar of ferroelectric material according to embodiments ofthe invention;

FIG. 2 is a cross-sectional view of a ferroelectric field effecttransistor (FEFET) according to embodiments of the invention;

FIG. 3 is a cross-sectional view of the FEFET of FIG. 2;

FIG. 4 is a cross-sectional view of a different embodiment of the FEFETshown in FIG. 2;

FIG. 5 shows write pulses and erase pulses applied to the bar offerroelectric material according to one or more embodiments of theinvention;

FIG. 6 shows the polarization curves that correspond with each readphase shown in FIG. 5;

FIG. 7 shows a multi-domain bar of ferroelectric material according toone or more embodiments of the invention;

FIG. 8 shows the process of obtaining a symmetric single domain wall barferroelectric according to one or more embodiments of the invention;

FIG. 9 shows an FEFET with a metal-ferro-silicon (MFS) structureaccording to one or more embodiments of the invention;

FIG. 10 shows an FEFET with an insulator layer below the barferroelectric according to one or more embodiments of the invention;

FIG. 11 shows an FEFET with five terminals according to one or moreembodiments of the invention;

FIG. 12 shows an FEFET with an insulator layer below the barferroelectric and five terminals according to one or more embodiments ofthe invention; and

FIG. 13 shows the read and write circuitry for an RPU element thatincludes a bar ferroelectric with a single domain wall according to oneor more embodiments of the invention.

DETAILED DESCRIPTION

As previously noted, RPUs are hardware memory devices that significantlyincrease the speed of memory access at lower voltages compared toconventional NVM devices. RPUs are physical analog memory components. AnRPU can be included in an array of thousands of memory elements (e.g.,4000-by-4000 elements) that can be used to simulate synapses insupervised learning, for example. Writing to an RPU memory element isaccomplished by applying an electric field pulse. A more challengingaspect of existing RPUs has involved accomplishing symmetry. Symmetryrefers to the fact that a pulse of the same amplitude used to write datato a memory element can also be used to erase the data in the memoryelement of the RPU. Symmetry of the RPU elements is an important factorin ensuring accuracy.

Turning now to an overview of one or more embodiments of the invention,a ferroelectric memory element is used to implement each memory elementof a symmetric RPU. A ferroelectric can be subjected to a spontaneouselectric polarization. A bar ferroelectric can be made to exhibit adifferent polarization at each end. The border between two differentpolarizations is referred to as the domain wall. A mobile ferroelectricsingle domain wall refers to the ability to move the domain wall thatseparates the two polarizations in a bar ferroelectric. The domain wallcan be moved by applying an electric field. This movement changes theconductance of a ferroelectric field effect transistor (FEFET) in whichthe bar ferroelectric is disposed between the channel and the gate. Theconductance can indicate a value such that affecting the conductance bymoving the domain wall results in the FEFET storing a particular datavalue. One or more embodiments of the invention described herein aredirected to a symmetric RPU memory element because the value written bymoving the domain wall based on applying a specific electric field canbe erased by applying a negative field of the same value.

Turning now to an exemplary embodiment of the invention, a barferroelectric 110 is shown in FIG. 1. Two portions 115 a, 115 b of thebar ferroelectric 110 are indicated. The two portions 115 a, 115 bexhibit opposite polarities, as indicated by the arrows in FIG. 1. Thepolarizations are achieved as discussed with reference to FIG. 2. Adomain wall 120 is used to indicate a border between the two portions115 a, 115 b of the bar ferroelectric 110 that have the oppositepolarities. When an electric field is applied across the barferroelectric 110, the domain wall 120 moves. That is, the dimensions ofthe two portions 115 a, 115 b are not fixed. Instead, based on theapplication of the electric field, the polarity of the bar ferroelectric110 on one side or the other of the domain wall 120 (in part 115 a or in115 b) changes. As such, the domain wall 120, which is an indication ofthe border between the two polarities, moves.

FIG. 2 is a cross-sectional view of an exemplary FEFET 200 which acts asan RPU element according to one or more embodiments. The substrate 210includes a channel region 215. The length L of the channel region 215 ison the order of 0.1 to 1 micrometers according to an exemplaryembodiment. The bar ferroelectric 110 is disposed between the channelregion 215 and a gate 230. Source 220 a and drain 220 b terminals areformed above doped regions 225 a, 225 b within the substrate 210. Aninsulator 235 acts as a spacer that separates the gate 230 from thesource 220 a and drain 220 b. In alternate embodiments, the source 220 aand drain 220 b can be reversed from the positions shown in FIG. 2. Inthe exemplary FEFET 200 shown in FIG. 2, the doped regions 225 a, 225 bare n++ doped. Applying the pinning voltages V+ and V− to the source 220a and drain 220 b terminals at each end of the bar ferroelectric 110results in the two portions 115 a and 115 b having opposite polarities.Applying an electric field across the bar ferroelectric 110 facilitatesmoving the domain wall 120. This is accomplished through the voltage VFEon the gate 230.

The position of the domain wall 120 determines the conductance of theFEFET 200. Thus, the conductance, which can be controlled by controllingthe position of the domain wall 120, can be used to read a value storedby the FEFET 200. The maximum conductance ratio, which is a ratio of theconductance achieved with the domain wall as close as possible to thesource 220 a to the conductance achieved with the domain wall as closeas possible to the drain 220 b, can be on the order of 10, for example.This determines the dynamic range of conductance values and correspondswith the values that can be stored by the RPU element.

The exemplary polarizations indicated for the portions 115 a, 115 b andthe relative position of the domain wall 120 in FIG. 2 indicate a higherconductance than if the domain wall 120 were closer to the drain 220 b.That is, the conductance is greater if the portion 115 a is smaller thanthe portion 115 b according to the polarity indicated in FIG. 2. Basedon the exemplary polarizations shown in FIG. 2 for portions 115 a and115 b, when VFE is a positive voltage, the domain wall 120 moves towardthe source 220 a, and when VFE is a negative voltage, the domain wall120 moves toward the drain 220 b. The voltage values needed for VFE canbe determined based on the coercive field Ec of the bar ferroelectric110, which is a measureable value for each bar ferroelectric 110.

The substrate 210 can include a bulk semiconductor, such as silicon,germanium, silicon germanium, silicon carbide, and those consistingessentially of III-V compound semiconductors having a compositiondefined by the formula Al_(X1)Ga_(X2)In_(X3)As_(Y1)P_(Y2)N_(Y3)Sb_(Y4),where X1, X2, X3, Y1, Y2, Y3, and Y4 represent relative proportions,each greater than or equal to zero and X1+X2+X3+Y1+Y2+Y3+Y4=1 (1 beingthe total relative mole quantity). Other suitable substrates 210 includeII-VI compound semiconductors having a compositionZn_(A1)Cd_(A2)Se_(B1)Te_(B2), where A1, A2, B1, and B2 are relativeproportions each greater than or equal to zero and A1+A2+B1+B2=1 (1being a total mole quantity). The semiconductor substrate 210 can alsoinclude an organic semiconductor or a layered semiconductor such as, forexample, Si/SiGe, a silicon-on-insulator or a SiGe-on-insulator. Aportion or entire semiconductor substrate 210 can be amorphous,polycrystalline, or monocrystalline. In addition to the aforementionedtypes of semiconductor substrates 210, the semiconductor substrate 210can also include a hybrid oriented (HOT) semiconductor substrate inwhich the HOT substrate has surface regions of differentcrystallographic orientation. The semiconductor substrate 210 can bedoped, undoped, or contain doped regions and undoped regions therein.The semiconductor substrate 210 can contain regions with strain andregions without strain therein, or contain regions of tensile strain andcompressive strain. In one or more embodiments, the substrate 210 can bea semiconductor-on-insulator (SOI) substrate. The substrate 210 canfurther include other structures (not shown) such as shallow trenchisolation (STI), fins, nanowires, nanosheets, resistors, capacitors,etc. The formation of the intermediate structure shown in FIG. 2 isknown and not further detailed herein.

FIG. 3 is a cross-sectional view of the FEFET 200 below the gate 230. AsFIG. 3 indicates, the two portions 115 a, 115 b of the bar ferroelectric110 are adjacent to each other and separated by the domain wall 120 inthe same plane as the source 220 a and drain 220 b. That is, only one ofthe portions 115 a, 115 b of the bar ferroelectric 110 is in contactwith the source 220 a or drain 220 b. Application of an electric fieldacross the bar ferroelectric 110 results in movement of the domain wall120 closer to either the source 220 a or the drain 220 b according tothe embodiment shown in FIG. 3.

FIG. 4 is a cross-sectional view of another embodiment of the FEFET 200below the gate 230. According to the embodiment shown in FIG. 4, the twoportions 115 a, 115 b of the bar ferroelectric 110 are adjacent to eachother and are separated by the domain wall 120 in a plane that isperpendicular to a plane of the source 220 a and drain 220 b. That is,both portions 115 a, 115 b of the bar ferroelectric 110 are in contactwith the source 220 a and the drain 220 b. Application of an electricfield across the bar ferroelectric 110 results in movement of the domainwall 120 along a side of the source 220 a and the drain 220 b accordingto the embodiment shown in FIG. 4. The width W is on the order of 0.1 to1 micrometers.

FIG. 5 shows write pulses 510 and erase pulses 520 applied to the barferroelectric 110 according to one or more embodiments of the invention.Time t is shown on one axis, as indicated, and pulse amplitude is shownon the other axis. E(t) is the applied pulse and E₀ is proportional tothe coercive field Ec of the bar ferroelectric 110. The write pulses 510are positive pulses E(t) and the erase pulses 520 are negative pulses ofthe same amplitude as the positive write pulses 510. This indicates thesymmetry of the FEFET 200. Several read phases 530 a through 530 f(generally referred to as 530) are indicated between the applications ofpulses. The conductance of the FEFET 200 can be determined during theread phase 530, and this conductance indicates the value stored by theFEFET 200. The read phases 530 are further discussed with reference toFIG. 6.

FIG. 6 shows the polarization curves 630 a through 630 e (generallyreferred to as 630) that correspond with each read phase 530 shown inFIG. 5. Distance along the bar ferroelectric 110 is shown on axis 610.The length of the exemplary bar ferroelectric 110 is 12 units.Polarization is shown on axis 620. The polarization curve 630 acorresponds with the read phase 530 a, prior to any pulses being appliedto the gate 230. After the first write pulse 510 is applied, the readphase 530 b results. As corresponding polarization curve 630 bindicates, the write pulse 510 causes a shift by a unit distance. Thatis, the domain wall 120 is moved such that the polarization that the barferroelectric 110 had at a given distance is now shifted by one unitdistance. As polarization curve 630 c, which corresponds with the readphase 530 c that follows another write pulse 510 indicates, the secondwrite pulse 510 results in another shift by a unit distance in thepolarization curve 630 c. Similarly, the polarization curve 630 d isshifted by a unit distance from the polarization curve 630 c. This isbecause polarization curve 630 d corresponds with read phase 530 d,which follows another (the third) write pulse 510 shown in FIG. 5.

Following the read phase 530 d, an erase pulse 520 is applied, as shownin FIG. 5. Because of the symmetry exhibited by the RPU element (e.g.,FEFET 200) that includes the bar ferroelectric 110, the erase pulse 520shifts the domain wall 120 back by one unit distance since each writepulse 510 shifted the domain wall 120 forward by one unit distance. Assuch, the polarization curve 630 e that corresponds with the read phase530 e following the first erase pulse 520 is the same as thepolarization curve 630 c, which characterized the bar ferroelectric 110prior to the last write pulse 510. A second erase pulse 520 precedes theread phase 530 f. This second erase pulse 520 shifts the domain wall 120back one unit distance again. As such, the polarization curve 630 f,which corresponds with read phase 530 f, is the same as the polarizationcurve 630 b, which characterized the bar ferroelectric 110 prior to thelast two write pulses 510.

FIG. 7 shows a multi-domain bar ferroelectric 110 according to one ormore embodiments of the invention. The bar ferroelectric 110 includesportions 115 a through 115 n (generally referred to as 115) separated bydomain walls 120-1 through 120-m (generally referred to as 120). A barferroelectric 110 with a single domain wall 120 is desirable because theconductance and, thus, the value stored by the RPU element iscontrollable based on controlling the position of the single domain wall120. Symmetry is more easily achieved with the single domain wall 120.However, in practice, when the pinning voltages V+ and V− are applied,the bar ferroelectric 110 with multiple portions 115 separated bymultiple domain walls 120 can result. The bar ferroelectric 110 withmultiple domain walls 120, as shown in FIG. 7, can be converted to barferroelectric 110 with a single domain wall 120, as shown in FIGS. 2-4,based on applying pulses of voltage VFE on the gate 230. As discussedwith reference to FIG. 5, applying pulses moves the domain wall 120 tochange the conductance of the FEFET 200, as well. This is furtherexplained with reference to FIG. 8.

FIG. 8 shows the process of obtaining a symmetric single domain wall 120bar ferroelectric 110 according to one or more embodiments. Aspreviously noted, the bar ferroelectric 110 can have multiple domainwalls 120 based on the application of pinning voltages V+ and V−, asshown in FIG. 7. As also previously discussed, with reference to FIGS. 5and 6, positive and negative pulses can be applied to a single domainwall 120 bar ferroelectric 110 to move the domain wall 120 in a knownand symmetric manner. This procedure is used to write and read valuesinto the RPU element that includes the bar ferroelectric 110.

However, when the bar ferroelectric 110 initially includes multipledomain walls 120, the symmetry needed to accurately write and readvalues from the RPU element is not present. FIG. 8 shows a curve 810indicating the polarization change over time as positive pulses arecontinually applied to a bar ferroelectric 110. As curve 810 shows,polarization change is gradual in region A. In region B, domain mergingoccurs and the multiple domain walls 120 merge into a single domain wall120 resulting in abrupt change of polarization. This single domain wall120 now separates regions of negative and positive polarization and isstabilized by opposite polarity of pinning boundaries. After this stage,in region C, the subsequent application of positive pulses results in alinear change in polarization, as shown. Specifically, the result ofapplying positive pulses is an increase in polarization, as shown.

In region C, the dashed line 820 indicates that, after sufficientpositive pulses have been applied to achieve the merge of multipledomain walls 120 into a single domain wall 120, the application ofnegative pulses (erase pulses) would result in the polarization stayingon the line shown in region C but decreasing rather than increasing. Thecontinued application of negative pulses would result in thepolarization decreasing along the dashed line 820 until the domain wallmoves to one end of the bar ferroelectric 110. Subsequent application ofpositive and negative pulses moves the polarization up and down alongthe dashed line 820. Of course, the negative pulses (and the resultingpolarization) that result in the polarization shown by dashed line 820would occur later in time than the range shown in FIG. 8. The barferroelectric 110 can be oriented as shown in FIG. 3 or FIG. 4. Ineither case, application of the positive pulses will result in the mergeof multiple domain walls 120 into a single domain wall 120 thatfacilitates the previously detailed symmetric write and eraseoperations.

FIGS. 9-12 show different embodiments of the FEFET that acts as an RPUelement according to one or more embodiments of the invention. AlthoughFIGS. 9-12 show a bar ferroelectric 110 according to the embodimentshown in FIG. 3, any of the embodiments shown in FIGS. 9-12 can also usethe bar ferroelectric according to the embodiment shown in FIG. 4. FIG.9 shows an FEFET 900 with a metal-ferro-silicon (MFS) structureaccording to one or more embodiments of the invention. That is, the barferroelectric 110 is under the source 220 a and drain 220 b terminalsand separates the source 220 a and drain 220 b terminals from the dopedregions 225 a, 225 b of the silicon substrate 210 according to theembodiment.

FIG. 10 shows an FEFET 1000 with an insulator layer 1010 below the barferroelectric 110 according to one or more embodiments of the invention.This embodiment can be thought of as including a metal-ferro-metal (MFM)top or a MFM in combination with a metal-insulator-silicon FET (MISFET).That is, the bar ferroelectric 110 is between the source 220 and drain220 b terminals and a quantum metal 1015 below the bar ferroelectric110. The quantum metal 1015 is doped Strontium Titanate, for example.While an electric field can penetrate the quantum metal 1015, having thequantum metal 1015 below and the metal of the gate 230 above the barferroelectric 110 results in more stable domains by lowering the domainenergy. The insulator layer 1010 is between the quantum metal 1015 andthe doped regions 225 a, 225 b of the silicon substrate 210. Theinsulator layer 1010 can be an oxide, nitride, or high-k dielectric, forexample.

FIG. 11 shows an FEFET 1100 with five terminals according to one or moreembodiments of the invention. The FEFET 1100 in FIG. 11 includes anotherset of spacers (insulator 235) and a pair of electrodes 1110. Based onthe arrangement of the embodiment shown in FIG. 11, the electrodes 1110include terminals to apply the pinning voltages V+ and V− to the barferroelectric 110. The source 220 a and drain 220 b additionally includeterminals. The pulses (VFE) to achieve a single domain wall 120 for thebar ferroelectric 110 and to move the domain wall 120 are appliedthrough the gate 230 terminal. As such, the FEFET 1100 includes fiveterminals. The conductance of the FEFET 1100 can be read directly usingthe terminals of the source 220 a and drain 220 b.

FIG. 12 shows an FEFET 1200 that is a MISFET with five terminalsaccording to one or more embodiments of the invention. Like theembodiment shown in FIG. 10, the FEFET 1200 includes an insulator layer1010 between the quantum metal 1015 and doped regions 225 a, 225 b ofthe silicon substrate 210. The FEFET 1200 also includes five terminalsas described for the FEFET 1100 shown in FIG. 11. This is based on theaddition of the electrodes 1110. As such, like the FEFET 1100 shown inFIG. 11, the FEFET 1200 shown in FIG. 12 facilitates sensing theconductance of the device and, thus, the value stored according tomovement of the domain wall 120 directly using the terminals of thesource 220 a and drain 220 b.

FIG. 13 shows the read and write circuitry for an RPU element 1300 thatincludes a bar ferroelectric 110 with a single domain wall 120 accordingto one or more embodiments of the invention. The RPU element 1300 can befabricated using an FEFET 200, 900, 1000, 1100, 1200 according to one ofthe embodiments shown in FIG. 2 or 9-12, for example. As previouslynoted, an RPU can include thousands of RPU elements 1300 (e.g., 5000 by5000 array), each of which includes circuitry to write and read values.As FIG. 13 indicates, pulses coincident on the I and W lines are inputat 1301 and 1302, respectively, to an AND gate 1310 and result in apulse being applied to the gate g of the RPU element 1300. As previouslydetailed, the pulse moves the domain wall 120 of the bar ferroelectric110 and changes the conductance of the RPU element 1300. The number ofpulses applied via the I and W lines determines the conductance set forthe RPU element 1300. Reading the conductance and, thus, the value setfor the RPU element 1300 involves grounding the I and W lines, applyinga small voltage between the J and R lines, and measuring the current,which is a measure of the conductance. Erasing the value written by thepulses applied over the I and W lines involves applying the same numberof negative pulses as positive pulses. This involves essentiallyreplacing the AND gate 1310 shown in FIG. 13 with a NAND gate. This isaccomplished with a circuit that is not shown in FIG. 13.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, element components,and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescription of the present invention has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the invention in the form described. Many modifications andvariations will be apparent to those of ordinary skill in the artwithout departing from the scope and spirit of the invention. Theembodiment was chosen and described in order to best explain theprinciples of the invention and the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated.

The flow diagrams depicted herein are just one example. There can bemany variations to this diagram or the steps (or operations) describedtherein without departing from the spirit of the invention. Forinstance, the steps can be performed in a differing order or steps canbe added, deleted or modified. All of these variations are considered apart of the claimed invention.

While the preferred embodiment to the invention had been described, itwill be understood that those skilled in the art, both now and in thefuture, can make various improvements and enhancements which fall withinthe scope of the claims which follow. These claims should be construedto maintain the proper protection for the invention first described.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments described. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdescribed herein.

What is claimed is:
 1. A method of fabricating a symmetric element of aresistive processing unit (RPU), the method comprising: forming asubstrate with a channel region connecting two doped regions; forming asource above one of the two doped regions and a drain above another ofthe two doped regions; forming a gate above the channel region; anddisposing a bar ferroelectric above the channel region and below thegate.
 2. The method according to claim 1, wherein forming the source andthe drain includes forming the source and the drain on the barferroelectric.
 3. The method according to claim 1, further comprisingforming an insulating layer on the channel region.
 4. The methodaccording to claim 3, wherein the disposing the bar ferroelectricincludes disposing the bar ferroelectric above the insulating layer suchthat the bar ferroelectric is separated from the channel region by theinsulating layer.
 5. The method according to claim 1, further comprisingforming a first electrode between the source and the gate and forming asecond electrode between the drain and the gate.
 6. The method accordingto claim 5, wherein the forming the first electrode and the secondelectrode includes forming the first electrode and the second electrodeabove the bar ferroelectric.
 7. The method according to claim 6, furthercomprising forming an insulating layer on the channel region.
 8. Themethod according to claim 7, wherein the disposing the bar ferroelectricincludes disposing the bar ferroelectric above the insulating layer suchthat the first electrode and the second electrode are formed above theinsulating layer.
 9. A method of obtaining a mobile ferroelectric singledomain wall implementation of a symmetric resistive processing unit(RPU), the method comprising: applying a positive pinning voltage to afirst end of a bar ferroelectric; applying a negative pinning voltage toa second end of the bar ferroelectric, wherein the second end isopposite the first end; applying positive pulses across the barferroelectric to achieve the single domain wall; and applying additionalpositive pulses across the bar ferroelectric to move the single domainwall in a first direction.
 10. The method according to claim 9, furthercomprising selecting an amplitude of the positive pulses and theadditional positive pulses based on a coercive field (Ec) of the barferroelectric.
 11. The method according to claim 9, further comprisingapplying negative pulses across the bar ferroelectric to move the singledomain wall in a second direction that is opposite to the firstdirection.
 12. The method according to claim 11, wherein the applyingthe negative pulses includes selecting a same amplitude as the positivepulses and the additional positive pulses.
 13. The method according toclaim 11, wherein each of the additional positive pulses moves thesingle domain wall a same distance in the first direction as each of thenegative pulses moves the single domain wall in the second direction.14. The method according to claim 9, wherein the applying the positivepulses, the additional positive pulses, and the negative pulses isthrough a gate of a field effect transistor in which the barferroelectric is disposed.
 15. A symmetric element of a resistiveprocessing unit (RPU), the element comprising: a substrate with achannel region connecting two doped regions; a source above one of thetwo doped regions; a drain above another of the two doped regions; agate above the channel region; and a bar ferroelectric above the channelregion and below the gate.
 16. The element according to claim 15,wherein the bar ferroelectric separates the source and the one of thetwo doped regions and the drain and the other of the two doped regions.17. The element according to claim 15, further comprising an insulatorlayer above the channel region that separates the channel region and thebar ferroelectric.
 18. The element according to claim 15, furthercomprising a first electrode between the source and the gate and asecond electrode between the drain and the gate, wherein the firstelectrode and the second electrode are above the bar ferroelectric. 19.The element according to claim 18, further comprising an insulator layerabove the channel region that separates the channel region from the barferroelectric and the first electrode and the second electrode above thebar ferroelectric.
 20. The element according to claim 17, furthercomprising a gate metal above the insulating layer, wherein the gatemetal separates the bar ferroelectric from the insulating layer.